That would depend on how much mathematics is in one's "standard sense."

Hello Doc!!! It's good to see you again!

Not to quibble overmuch, but I think Bohr was using the word "visualizable" in its "standard sense": What is "visualizable" is what comes into our consciousness by means of the "inputs" of sensory perception. His point is that this sort of thing is what shapes the categories of human thought that inevitably translates into such conceptions as the physical laws. In other words, our immediate perceptions of space and time condition how we think.

Now mathematics does not work thataway. It has nothing to do with sensory perception, or the "visualizations" we can describe based on sensory perception. It seems to me that mathematics is extraordinarily "non-visual": It allows us to formulate conceptions about things that are "unseen." If i might put it that way.

Not visualization is involved here, but conceptualization. Which tells you that "material inputs to the brain via the eyes as stimulated by external phenomena" is not the whole story of how the mind works. Mathematics is unimpeachable evidence of this.

Anyhoot, I just love what Eugene Wigner had to say on this point:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research.

And I hope so, too, dear Doc, with all my heart.

Thanks so much for writing T. -- it's good to hear from you.

101
posted on 09/16/2006 6:09:09 PM PDT
by betty boop
(Beautiful are the things we see...Much the most beautiful those we do not comprehend. -- N. Steensen)

It has nothing to do with sensory perception, or the "visualizations" we can describe based on sensory perception. It seems to me that mathematics is extraordinarily "non-visual": It allows us to formulate conceptions about things that are "unseen." If i might put it that way.

One may describe many things mathematically. Some people visualize these; others may not. I tend to visualize most mathematical items. Certainly things in vector spaces or arithmetic have a visual component.

"It's not the future which is indeterminate, but the past." Actually, could we say that to a finite living observer that may be so, but the universe has no problem with the deterministic state of past, because it (the event as present when it happened) is entangled with the origin of the universe itself? To imply that the cat died at 4 but is in superposition until an observer notes the cat, is a false assertion (else nothing would have 'finished' prior to living observers being in the universe; everything would have been in superposition from the big bang onward, until living observers arrived, somehow). The universe is 'an' observer (because past and present exist in simultaneity in which the event of death occurred) but superposition is a temporal problem for the finite living observer due to the nature of the observers fix in time as always in 'planar' present while alive, yet sensing ONLY events that have already occurred. I like, for thought purposes, to think of past as linear and the ends of each pathway form the plane of present, with the 'blossom' of future the 'every path possible from present' on the opposite side of the planar present from the linear past.

106
posted on 09/16/2006 8:50:57 PM PDT
by MHGinTN
(If you can read this, you've had life support from someone. Promote life support for others.)

"Remember that, according to Heisenberg, the path of an object first comes into existence when we observe it. By choosing either the wave or the particle picture, the experimenter disturbs untouched nature." 'Untouched nature' has both past and present temporal location, so the 'disturbing' is catually dividing the variable expressions of dimension time in favor of one or the other (particle=past; wave=present) as a bias of observation. But prior to there being any living observer for phenomena in the universe, the universe acted as observer, so superposition is a temporal phenomenon (past and present undivided) due to the nature of the universe now mixing dimension space and dimension time in the variable expressions of each dimension, to generate continuua of space/time//time/space expression states. The fundamental forces we define have yet to be expressed as favoring a temporal bias or a spatial bias ... and that's what I'm working on in my own feeble way, don'tchaknow.

108
posted on 09/16/2006 9:01:25 PM PDT
by MHGinTN
(If you can read this, you've had life support from someone. Promote life support for others.)

[ I like, for thought purposes, to think of past as linear and the ends of each pathway form the plane of present, with the 'blossom' of future the 'every path possible from present' on the opposite side of the planar present from the linear past. ]

I like to be in the moment.. All past and future is/are composed of moments.. You handle the current moment correctly/wisely (as wisely as you can) and the past and future will take care of themselves.. Life is more about timeing than about time.. I think Jesus said the same thing in another way.. Time is probably not very important to eternal beings.. but timing is always important..

110
posted on 09/16/2006 9:36:10 PM PDT
by hosepipe
(CAUTION: This propaganda is laced with hyperbole.)

else nothing would have 'finished' prior to living observers being in the universe; everything would have been in superposition from the big bang onward, until living observers arrived, somehow

I didn't understand most of what you were trying to say, but QM in no way requires an observer to be "living" or "intelligent" or "conscious". Any in-practice transfer of information will do. That's why quantum computers are so fussy to construct: the qubits decohere at much less than the drop of a hat, and it's not because somebody's peeking.

Your determinism probably does work in the case of a real cat, because it's so difficult to isolate from all information transfer that the state collapses more or less instantly. In the case of a subatomic particle, however isolation is much more likely, and your determinism explicitly fails (as seen in the Aspect experiment).

I think I stated that the universe IS the observer. But the universe observes differently than we and our measuring devices do ... past and present have simultaneous existence from the universe's perspective.

112
posted on 09/16/2006 9:41:18 PM PDT
by MHGinTN
(If you can read this, you've had life support from someone. Promote life support for others.)

Not useful. If it were an observer in the QM sense, then there would never be quantum superposition, but we know as an experimental matter that superposition occurs. So you must mean "observer" in some other sense.

I'm not a Physicist, but I think the quantum field acts as a continuous observer, entangling every mass with the entire mass of the universe in a temporal fashion, while 'measuring' the spatial relationship of each and every mass to the entire mass of the universe.

114
posted on 09/16/2006 10:09:17 PM PDT
by MHGinTN
(If you can read this, you've had life support from someone. Promote life support for others.)

If we were to think of time as a space divided into two halves. One being the future and the other the the past. We exist on the plane that separates them. We can not see, touch, smell or feel the future anymore than we can the past. We can only sense the present, remember the past and extrapolate the future from the past to the present(this helps with walking as we can see where we came from and where we are now and figure we are going to keep going in the same direction). The question is, does the present have any depth to it?

IOW is it just the 2 dimensional boundary between the past and future or is there a third dimensional quality to it where it encompasses both future and past?

Just some fuzzy thoughts to nod off with.

115
posted on 09/16/2006 10:51:21 PM PDT
by Boiler Plate
(Mom always said why be difficult, when with just a little more effort you can be impossible.)

..."material inputs to the brain via the eyes as stimulated by external phenomena" is not the whole story of how the mind works.

You, and your words: Gems. Many thanks for sharing your insights with me. Our Lord of Grace and Truth continue His blessing to thee in Christ Jesus His Son and keep you blessing others continually as you do here!

I tend to visualize most mathematical items. Certainly things in vector spaces or arithmetic have a visual component.

But of course, Doc! But the point is that "visualization" involves the categories of space and time; and these are formed in our minds on the basis of sensory experience. I think this is what Niels Bohr was getting at. He was amazingly rigorous, epistemologically speaking.

119
posted on 09/17/2006 10:09:56 AM PDT
by betty boop
(Beautiful are the things we see...Much the most beautiful those we do not comprehend. -- N. Steensen)

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